Translate the following sentences into wfs 1x is transcenden

Translate the following sentences into wfs.

1.x is transcendental only if it is irrational.

2. If anyone can solve the problem, Hilary can.

3. Nobody loves a loser.

4. Everyone loves somebody and no one loves everybody, or somebody loves everybody and someone loves nobody.

5. Any sets that have the same members are equal.

Answer :

1. Consider the given statement \" x is transcendental only if it is irrational \".

Let us denote P(x) : x is irrational

Q(x) : x is transcendental

Then statement ( 1) can be wrietten as x ( P(x) Q(x) )

2. Consider the given statement \" If anyone can solve the problem, Hilary can. \".

Let us denote P(x) : x can solve the problem

H: Hilary

Then statement ( 2) can be wrietten as x ( P(x) P(H) )

3.Consider the given statement \" Nobody loves a loser\".

Let us denote P(x) : x loves loser

Then statement ( 3) can be wrietten as x ¬ P(x)

4.Consider the given statement \" Everyone loves somebody and no one loves everybody, or somebody loves everybody and someone loves nobody \"

Let us denote

P(x,y) : x loves y

Then statement ( 4 ) can be wrietten as

( x y P(x,y) x y ¬P(x,y) ) V ( x y P(x,y) x y ¬ P(x,y) )

5. Consider the given statement \" Any sets that have the same members are equal \".

Let us denote

P(x,y) : x , y are sets

Q(x,y) : x and y have same memebers

R(x ,y) : x and y are equal

Then statement ( 5 ) can be wrietten as

x y ( (P(x,y) Q(x,y) ) R(x ,y) )